CBSE Class 11 Physics Worksheet Set E Solved

1. State the theorem of parallel axes for moment of inertia. 

2. Particle of mass 0.4Kg is moving in a circle of radius 0.5m with frequency4/π S^-1. Find its angular momentum.

3. While turning the page of book, we usually apply force perpendicular to the plane of the page at the farthest end. Explain why?

4. Which physical quantity is represented by the product of moment of inertia and angular acceleration?

5. Explain why the speed of whirl wind in a tornado is alarmingly high? 

6. Three balls of masses 1, 2 and 3Kg respectively are arranged at the corners of an equilateral triangle of side 1m.What will be the M.I. of the system about an axis through the centroid and perpendicular to the plane of triangle?

7. Define and explain the principle of moments. 

8. Derive an expression showing the relation between angular momentum and moment of inertia of a rigid body.

9. What will be the duration of the day, if the earth suddenly shrinks to 1/64 of its original volume but mass of earth remains unchanged? Given moment of inertia of the earth = 2/5 MR².

10. Define moment of inertia. Write its SI units and dimensional formula. State the factors on which moment of inertia of a body depends.

11. Derive an expression for the total kinetic energy of a rolling body. Write an expression for total kinetic energy of a rolling solid sphere whose mass m and radius r.

VALUE POINTS

1. Monet of inertia of a body about any axis in its plane and parallel to an axis passing through the centre of mass of the body is equal to its moment of inertia about an axis passing through the centre of mass of the body plus the product of the mass of the body and square of the distance between the two axes.

2. w = 8 rad s^-1, v = rw =0.5 X 8 = 4ms^-1, L = mvr L = 0.8Kgm2s^-1

3. When the page is turned, it rotates about the bound end of the book. By applying the force at right angle to the farthest end of the page of the page, maximum torque is produced. Thus the page can be turned easily even on applying a small force.

4. Torque

5. The inner layers of the whirl wind in a tornado are closer to the axis of rotation. It means, the moment of inertia of the air molecules of inner layers is small. Hence, according to the law of conservation of angular momentum, the angular speed of the whirl wind In a tornado is very high.

6. I=(m₁+m₂+m₃)r²=(1+2+3)×(1√3)²=2kgm² 

7. The principle of moments states that, when an object is in equilibrium, the sum of anticlockwise moments about any point equals the sum of clockwise moments about the same point.

The moment of a force about any point is defined as the force x perpendicular distance from the line of action of the force to the point - moment = F x d F₁d₁ = F₂d₂ or W₁d₁ = W₂d₂, where W is weight.

8. Derivation for the relation between the angular momentum and moment of inertia.
L = IW

9. V´=V/64 So the radius r´of the shrunk earth is
r´= r/4
from the principle of conservation of angular momentum
I´ω´＝Iω

ω´＝Iω /I´=(r/r´)²X ω=16ω
here I means moment of inertia
( I´＝２M(r´²)/5, I＝２M(r²)/5)
T: Duration of the day
T=24hours
T´=2π/ω´=2π/16ω=T/16
=1.5hours

10. Definition of M.I.
SI unit: Kgm² ( M¹L²T ⁰)
Any two factors

11. Derivation for total kinetic energy of rolling body:
Ek = ½ mv²(1 + I/mr²)
Total Kinetic energy of rolling solid sphere:
Ek= 7/10 mv

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